Look, I make no excuses for using my kids as case study subjects, experiments, or sample sizes. Their minds are ripe for the taking and I'm going to take advantage of two kids who are in the early stages of their educational careers (Kinder and Pre-school). Whew... not that this is out the way, let's have some fun.

As I'm writing lessons for using a 3D printer in the classroom, I'm trying to think of ways that kids could really have fun with it while seeing a strong educational benefit. In this lesson, the students are being asked to create four sets of equivalent fractions. Later, they will print them out and use those groups to answer a series of questions. Since my son isn't old enough to design the objects, I did, then we printed them.

Once the little one went down for a nap, my oldest son and I started playing. The first task was to create the half block using any of the others, but not another half block.

Almost immediately, he reached for the two quarter blocks, lined them up neatly, then smiled. I didn't want anything to get lost along the way, so we wrote our observations:

We noticed that there were zero full blocks, zero half blocks, two quarter blocks, and zero sixteenth blocks. He looked up, smiled again, then said

"come on daddy, give me one that's harder. That was too easy!"

​Challenge accepted.

"Try to make three fourths," I said, as I put the half and quarter​ block together.

The only rule was that he couldn't use another half block, but that didn't stop him. Within seconds of looking at his options, he gathered up the sixteenths, added in a quarter, and assembled them.

"Come on daddy, I thought you were going to give me a hard one!"

​"Hold on buddy, we still need to write it down."

We wrote it down, talked about how three fourths is the same as one fourth plus eight sixteenths (although I'm certain that it went over his head), then got into the challenge.

I'm not going to claim that my son now understands that:

one plus one half plus two sixteenths = four fourths plus ten sixteenths

What I am going to claim is that my son was playing around with equivalent fractions, wasn't afraid of them, and thought that they were easy. If we can do things like this throughout a child's education, maybe the math monster won't be so scary as they progress through school... or maybe it's all a bunch of blocks.

What could you do with this lesson? How would you change it? I'm interested in your feedback.

Wow, Jason! Thank you for sharing. Not going to lie, when I first saw the post about equivalent fractions, I was like, oh that's for big kids, so I kept going... I was thinking something different about your work with your kiddos. (Mine are crash test dummies too BTW.) I was noticing how your child is already forming ideas of how something bigger can be made of different combinations of smaller parts. Thinking about composing and decomposing numbers and hierarchical inclusion. I love that the cuisenaire rods are not labeled, thinking any size can become the whole. There is a good opportunity here for discussion on equal parts which will later serve as a basis for multiplication, division and fractions. Fun stuff! How did you get your hands on a 3D printer?

Reply

Fletch

2/20/2016 09:30:35 am

I really like this idea of having students create the tool. Many times we just throw manipulatives at our students and tell them how to use them without ever providing an opportunity to explore or construct.
I'm assuming that by allowing students to create the set, as you've suggested here, they'll begin to see and employ tools more flexibly going forward. Example...what if we assign the quarter cube in your set a value of 2/3? What's the value of the large square?
You have me wondering what other opportunities we can provide students to create their own manipulatives.